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Currently I am using OpenCart in an attempt to accomplish something similar but I keep running into problems as far as functionality.

Basically what I'm after is a platform that allows for a list of product options each with a quantity box to the side and each with different variable pricing. I also need a function that allows the price to be different based on different customer groups e.g. different prices for school accounts.

I don't know any existing platform that provide this options. The site you provided as example runs on windows, and it might be on ASP.net.
If you don't find anything similar, contact me, I can build you one based on your needs, at a good price.